Observation of antiphase coherent phonons in the warped Dirac cone of Bi${}_2$Te${}_3$

In this Rapid Communication we investigate the coupling between excited electrons and phonons in the highly anisotropic electronic structure of the prototypical topological insulator Bi${}_2$Te${}_3$. Using time- and angle-resolved photoemission spectroscopy we are able to identify the emergence and ultrafast temporal evolution of the longitudinal-optical A${}_{1g}$ coherent-phonon mode in Bi${}_2$Te${}_3$. We observe an antiphase behavior in the onset of the coherent-phonon oscillations between the $\overline{\mathrm{\Gamma }K}$ and the $\overline{\mathrm{\Gamma }M}$ high-symmetry directions that is consistent with warping. The qualitative agreement between our density-functional theory calculations and the experimental results reveals the critical role of the anisotropic coupling between Dirac fermions and phonon modes in the topological insulator Bi${}_2$Te${}_3$.